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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 30 Nov 2008 11:59:06 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/30/t1228071854i9dbvgxf39ziy0l.htm/, Retrieved Tue, 14 May 2024 17:07:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26692, Retrieved Tue, 14 May 2024 17:07:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact196

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Q1 central tenden...] [2007-10-18 09:40:43] [b731da8b544846036771bbf9bf2f34ce]
F    D  [Central Tendency] [task 3 Q1 Reprodu...] [2008-10-19 12:06:44] [86761fc994bdf34e4f4ab5b8e1d9e1c3]
-    D    [Central Tendency] [CT Bouwproductie] [2008-11-30 18:25:17] [aa5573c1db401b164e448aef050955a1]
- R           [Central Tendency] [Central Tendancy ...] [2008-11-30 18:59:06] [8a1195ff8db4df756ce44b463a631c76] [Current]
- R  D          [Central Tendency] [Central Tendancy ...] [2008-11-30 19:21:14] [aa5573c1db401b164e448aef050955a1]
-    D            [Central Tendency] [CT Investeringen] [2008-11-30 21:15:30] [aa5573c1db401b164e448aef050955a1]
- R                 [Central Tendency] [CT invest gemiddelde] [2008-11-30 21:32:45] [aa5573c1db401b164e448aef050955a1]
-    D              [Central Tendency] [CT omzet ] [2008-11-30 21:40:40] [aa5573c1db401b164e448aef050955a1]
- R                   [Central Tendency] [CT omzet gemiddelde] [2008-11-30 21:44:33] [aa5573c1db401b164e448aef050955a1]
- R                   [Central Tendency] [CT Gemiddelde omzet] [2008-11-30 22:36:39] [aa5573c1db401b164e448aef050955a1]
- RM D                [Univariate Explorative Data Analysis] [Univariate EDA Bo...] [2008-11-30 23:26:57] [aa5573c1db401b164e448aef050955a1]
- RM D                [Univariate Explorative Data Analysis] [Univariate EDA To...] [2008-11-30 23:51:28] [aa5573c1db401b164e448aef050955a1]
- RM D                [Univariate Explorative Data Analysis] [Univariate EDA In...] [2008-11-30 23:58:42] [aa5573c1db401b164e448aef050955a1]
- RM                  [Univariate Explorative Data Analysis] [Univariate EDA Omzet] [2008-12-01 00:05:10] [aa5573c1db401b164e448aef050955a1]
- RM D                [Univariate Explorative Data Analysis] [Univariate EDA In...] [2008-12-01 00:12:08] [aa5573c1db401b164e448aef050955a1]
- R  D            [Central Tendency] [CT gemiddelde invest] [2008-11-30 21:19:41] [aa5573c1db401b164e448aef050955a1]
- R  D          [Central Tendency] [Central Tendancy ...] [2008-11-30 19:24:23] [aa5573c1db401b164e448aef050955a1]
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Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
82.7
88.9
105.9
100.8
94
105
58.5
87.6
113.1
112.5
89.6
74.5
82.7
90.1
109.4
96
89.2
109.1
49.1
92.9
107.7
103.5
91.1
79.8
71.9
82.9
90.1
100.7
90.7
108.8
44.1
93.6
107.4
96.5
93.6
76.5
76.7
84
103.3
88.5
99
105.9
44.7
94
107.1
104.8
102.5
77.7
85.2
91.3
106.5
92.4
97.5
107
51.1
98.6
102.2
114.3
99.4
72.5
92.3
99.4
85.9
109.4
97.6

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26692&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26692&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26692&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-1.10410211956031e-142.01549348282001-5.47807337990239e-15
Geometric MeanNaN
Harmonic Mean-107.722575634686
Quadratic Mean16.1239478625601
Winsorized Mean ( 1 / 21 )-0.00923076923078032.00894988980893-0.00459482303546069
Winsorized Mean ( 2 / 21 )0.1076923076922971.958045778124400.0549998926968167
Winsorized Mean ( 3 / 21 )0.0569230769230661.904737165238040.0298850035385077
Winsorized Mean ( 4 / 21 )0.5123076923076821.760307598187510.291033051743443
Winsorized Mean ( 5 / 21 )1.519999999999991.483251216617611.02477583228698
Winsorized Mean ( 6 / 21 )1.547692307692301.466294059604271.05551290858397
Winsorized Mean ( 7 / 21 )1.644615384615371.400492648950121.17431204358571
Winsorized Mean ( 8 / 21 )1.853846153846141.344231402002711.37911236940617
Winsorized Mean ( 9 / 21 )1.839999999999991.332107403003261.3812700055954
Winsorized Mean ( 10 / 21 )1.978461538461531.299655507382561.52229689115545
Winsorized Mean ( 11 / 21 )2.249230769230761.219630485315151.84419034807052
Winsorized Mean ( 12 / 21 )2.673846153846141.108892979080152.41127521256754
Winsorized Mean ( 13 / 21 )2.673846153846141.108892979080152.41127521256754
Winsorized Mean ( 14 / 21 )2.523076923076911.070826942244492.35619484674942
Winsorized Mean ( 15 / 21 )2.730769230769221.022280560501222.67125223376088
Winsorized Mean ( 16 / 21 )2.706153846153840.9258075796601652.92301975659692
Winsorized Mean ( 17 / 21 )2.836923076923070.8896253616122173.18889635945391
Winsorized Mean ( 18 / 21 )3.086153846153830.7860731649853343.92603892821022
Winsorized Mean ( 19 / 21 )3.261538461538450.7357011207367124.43323840294334
Winsorized Mean ( 20 / 21 )2.953846153846140.6540600894349964.51616938804169
Winsorized Mean ( 21 / 21 )3.018461538461530.6360633248776714.74553620748696
Trimmed Mean ( 1 / 21 )0.3972161172161061.90074595845830.208979067112308
Trimmed Mean ( 2 / 21 )0.8303152585119691.765797485458740.470221112754761
Trimmed Mean ( 3 / 21 )1.228370273793991.632258314186770.752558748279983
Trimmed Mean ( 4 / 21 )1.6736572199731.489759191059561.12344144611898
Trimmed Mean ( 5 / 21 )2.016783216783211.373671804733461.46816962380219
Trimmed Mean ( 6 / 21 )2.138635703918711.332134985122981.60541966677744
Trimmed Mean ( 7 / 21 )2.264162895927591.284998171160041.76199697925141
Trimmed Mean ( 8 / 21 )2.381569858712701.244420910604151.91379768566930
Trimmed Mean ( 9 / 21 )2.472798690671021.208067158795822.04690498592468
Trimmed Mean ( 10 / 21 )2.574358974358961.163912767046112.21181436207837
Trimmed Mean ( 11 / 21 )2.664436493738811.114983213324082.38966511952711
Trimmed Mean ( 12 / 21 )2.724277673545951.072265416369002.54067475455018
Trimmed Mean ( 13 / 21 )2.731282051282041.044371811856652.6152391516834
Trimmed Mean ( 14 / 21 )2.739043659043651.005716555553522.72347476425517
Trimmed Mean ( 15 / 21 )2.767692307692300.9625491365827172.87537768463257
Trimmed Mean ( 16 / 21 )2.772540792540780.916082333165893.02651922448843
Trimmed Mean ( 17 / 21 )2.781240694789070.8790994351365723.16373846191471
Trimmed Mean ( 18 / 21 )2.773899204244020.835860727697313.31861410917793
Trimmed Mean ( 19 / 21 )2.732136752136740.805630706780413.39130165861644
Trimmed Mean ( 20 / 21 )2.659692307692300.7746078577792343.43359840851281
Trimmed Mean ( 21 / 21 )2.618127090300990.7553612015235773.46605979367246
Median1.88769230769229
Midrange-12.5123076923077
Midmean - Weighted Average at Xnp2.49081730769230
Midmean - Weighted Average at X(n+1)p2.77254079254078
Midmean - Empirical Distribution Function2.77254079254078
Midmean - Empirical Distribution Function - Averaging2.77254079254078
Midmean - Empirical Distribution Function - Interpolation2.77254079254078
Midmean - Closest Observation2.46416289592759
Midmean - True Basic - Statistics Graphics Toolkit2.77254079254078
Midmean - MS Excel (old versions)2.77254079254078
Number of observations65

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -1.10410211956031e-14 & 2.01549348282001 & -5.47807337990239e-15 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -107.722575634686 &  &  \tabularnewline
Quadratic Mean & 16.1239478625601 &  &  \tabularnewline
Winsorized Mean ( 1 / 21 ) & -0.0092307692307803 & 2.00894988980893 & -0.00459482303546069 \tabularnewline
Winsorized Mean ( 2 / 21 ) & 0.107692307692297 & 1.95804577812440 & 0.0549998926968167 \tabularnewline
Winsorized Mean ( 3 / 21 ) & 0.056923076923066 & 1.90473716523804 & 0.0298850035385077 \tabularnewline
Winsorized Mean ( 4 / 21 ) & 0.512307692307682 & 1.76030759818751 & 0.291033051743443 \tabularnewline
Winsorized Mean ( 5 / 21 ) & 1.51999999999999 & 1.48325121661761 & 1.02477583228698 \tabularnewline
Winsorized Mean ( 6 / 21 ) & 1.54769230769230 & 1.46629405960427 & 1.05551290858397 \tabularnewline
Winsorized Mean ( 7 / 21 ) & 1.64461538461537 & 1.40049264895012 & 1.17431204358571 \tabularnewline
Winsorized Mean ( 8 / 21 ) & 1.85384615384614 & 1.34423140200271 & 1.37911236940617 \tabularnewline
Winsorized Mean ( 9 / 21 ) & 1.83999999999999 & 1.33210740300326 & 1.3812700055954 \tabularnewline
Winsorized Mean ( 10 / 21 ) & 1.97846153846153 & 1.29965550738256 & 1.52229689115545 \tabularnewline
Winsorized Mean ( 11 / 21 ) & 2.24923076923076 & 1.21963048531515 & 1.84419034807052 \tabularnewline
Winsorized Mean ( 12 / 21 ) & 2.67384615384614 & 1.10889297908015 & 2.41127521256754 \tabularnewline
Winsorized Mean ( 13 / 21 ) & 2.67384615384614 & 1.10889297908015 & 2.41127521256754 \tabularnewline
Winsorized Mean ( 14 / 21 ) & 2.52307692307691 & 1.07082694224449 & 2.35619484674942 \tabularnewline
Winsorized Mean ( 15 / 21 ) & 2.73076923076922 & 1.02228056050122 & 2.67125223376088 \tabularnewline
Winsorized Mean ( 16 / 21 ) & 2.70615384615384 & 0.925807579660165 & 2.92301975659692 \tabularnewline
Winsorized Mean ( 17 / 21 ) & 2.83692307692307 & 0.889625361612217 & 3.18889635945391 \tabularnewline
Winsorized Mean ( 18 / 21 ) & 3.08615384615383 & 0.786073164985334 & 3.92603892821022 \tabularnewline
Winsorized Mean ( 19 / 21 ) & 3.26153846153845 & 0.735701120736712 & 4.43323840294334 \tabularnewline
Winsorized Mean ( 20 / 21 ) & 2.95384615384614 & 0.654060089434996 & 4.51616938804169 \tabularnewline
Winsorized Mean ( 21 / 21 ) & 3.01846153846153 & 0.636063324877671 & 4.74553620748696 \tabularnewline
Trimmed Mean ( 1 / 21 ) & 0.397216117216106 & 1.9007459584583 & 0.208979067112308 \tabularnewline
Trimmed Mean ( 2 / 21 ) & 0.830315258511969 & 1.76579748545874 & 0.470221112754761 \tabularnewline
Trimmed Mean ( 3 / 21 ) & 1.22837027379399 & 1.63225831418677 & 0.752558748279983 \tabularnewline
Trimmed Mean ( 4 / 21 ) & 1.673657219973 & 1.48975919105956 & 1.12344144611898 \tabularnewline
Trimmed Mean ( 5 / 21 ) & 2.01678321678321 & 1.37367180473346 & 1.46816962380219 \tabularnewline
Trimmed Mean ( 6 / 21 ) & 2.13863570391871 & 1.33213498512298 & 1.60541966677744 \tabularnewline
Trimmed Mean ( 7 / 21 ) & 2.26416289592759 & 1.28499817116004 & 1.76199697925141 \tabularnewline
Trimmed Mean ( 8 / 21 ) & 2.38156985871270 & 1.24442091060415 & 1.91379768566930 \tabularnewline
Trimmed Mean ( 9 / 21 ) & 2.47279869067102 & 1.20806715879582 & 2.04690498592468 \tabularnewline
Trimmed Mean ( 10 / 21 ) & 2.57435897435896 & 1.16391276704611 & 2.21181436207837 \tabularnewline
Trimmed Mean ( 11 / 21 ) & 2.66443649373881 & 1.11498321332408 & 2.38966511952711 \tabularnewline
Trimmed Mean ( 12 / 21 ) & 2.72427767354595 & 1.07226541636900 & 2.54067475455018 \tabularnewline
Trimmed Mean ( 13 / 21 ) & 2.73128205128204 & 1.04437181185665 & 2.6152391516834 \tabularnewline
Trimmed Mean ( 14 / 21 ) & 2.73904365904365 & 1.00571655555352 & 2.72347476425517 \tabularnewline
Trimmed Mean ( 15 / 21 ) & 2.76769230769230 & 0.962549136582717 & 2.87537768463257 \tabularnewline
Trimmed Mean ( 16 / 21 ) & 2.77254079254078 & 0.91608233316589 & 3.02651922448843 \tabularnewline
Trimmed Mean ( 17 / 21 ) & 2.78124069478907 & 0.879099435136572 & 3.16373846191471 \tabularnewline
Trimmed Mean ( 18 / 21 ) & 2.77389920424402 & 0.83586072769731 & 3.31861410917793 \tabularnewline
Trimmed Mean ( 19 / 21 ) & 2.73213675213674 & 0.80563070678041 & 3.39130165861644 \tabularnewline
Trimmed Mean ( 20 / 21 ) & 2.65969230769230 & 0.774607857779234 & 3.43359840851281 \tabularnewline
Trimmed Mean ( 21 / 21 ) & 2.61812709030099 & 0.755361201523577 & 3.46605979367246 \tabularnewline
Median & 1.88769230769229 &  &  \tabularnewline
Midrange & -12.5123076923077 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.49081730769230 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.77254079254078 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.77254079254078 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.77254079254078 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.77254079254078 &  &  \tabularnewline
Midmean - Closest Observation & 2.46416289592759 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.77254079254078 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.77254079254078 &  &  \tabularnewline
Number of observations & 65 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26692&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]-1.10410211956031e-14[/C][C]2.01549348282001[/C][C]-5.47807337990239e-15[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-107.722575634686[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]16.1239478625601[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 21 )[/C][C]-0.0092307692307803[/C][C]2.00894988980893[/C][C]-0.00459482303546069[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 21 )[/C][C]0.107692307692297[/C][C]1.95804577812440[/C][C]0.0549998926968167[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 21 )[/C][C]0.056923076923066[/C][C]1.90473716523804[/C][C]0.0298850035385077[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 21 )[/C][C]0.512307692307682[/C][C]1.76030759818751[/C][C]0.291033051743443[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 21 )[/C][C]1.51999999999999[/C][C]1.48325121661761[/C][C]1.02477583228698[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 21 )[/C][C]1.54769230769230[/C][C]1.46629405960427[/C][C]1.05551290858397[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 21 )[/C][C]1.64461538461537[/C][C]1.40049264895012[/C][C]1.17431204358571[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 21 )[/C][C]1.85384615384614[/C][C]1.34423140200271[/C][C]1.37911236940617[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 21 )[/C][C]1.83999999999999[/C][C]1.33210740300326[/C][C]1.3812700055954[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 21 )[/C][C]1.97846153846153[/C][C]1.29965550738256[/C][C]1.52229689115545[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 21 )[/C][C]2.24923076923076[/C][C]1.21963048531515[/C][C]1.84419034807052[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 21 )[/C][C]2.67384615384614[/C][C]1.10889297908015[/C][C]2.41127521256754[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 21 )[/C][C]2.67384615384614[/C][C]1.10889297908015[/C][C]2.41127521256754[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 21 )[/C][C]2.52307692307691[/C][C]1.07082694224449[/C][C]2.35619484674942[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 21 )[/C][C]2.73076923076922[/C][C]1.02228056050122[/C][C]2.67125223376088[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 21 )[/C][C]2.70615384615384[/C][C]0.925807579660165[/C][C]2.92301975659692[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 21 )[/C][C]2.83692307692307[/C][C]0.889625361612217[/C][C]3.18889635945391[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 21 )[/C][C]3.08615384615383[/C][C]0.786073164985334[/C][C]3.92603892821022[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 21 )[/C][C]3.26153846153845[/C][C]0.735701120736712[/C][C]4.43323840294334[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 21 )[/C][C]2.95384615384614[/C][C]0.654060089434996[/C][C]4.51616938804169[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 21 )[/C][C]3.01846153846153[/C][C]0.636063324877671[/C][C]4.74553620748696[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 21 )[/C][C]0.397216117216106[/C][C]1.9007459584583[/C][C]0.208979067112308[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 21 )[/C][C]0.830315258511969[/C][C]1.76579748545874[/C][C]0.470221112754761[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 21 )[/C][C]1.22837027379399[/C][C]1.63225831418677[/C][C]0.752558748279983[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 21 )[/C][C]1.673657219973[/C][C]1.48975919105956[/C][C]1.12344144611898[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 21 )[/C][C]2.01678321678321[/C][C]1.37367180473346[/C][C]1.46816962380219[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 21 )[/C][C]2.13863570391871[/C][C]1.33213498512298[/C][C]1.60541966677744[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 21 )[/C][C]2.26416289592759[/C][C]1.28499817116004[/C][C]1.76199697925141[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 21 )[/C][C]2.38156985871270[/C][C]1.24442091060415[/C][C]1.91379768566930[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 21 )[/C][C]2.47279869067102[/C][C]1.20806715879582[/C][C]2.04690498592468[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 21 )[/C][C]2.57435897435896[/C][C]1.16391276704611[/C][C]2.21181436207837[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 21 )[/C][C]2.66443649373881[/C][C]1.11498321332408[/C][C]2.38966511952711[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 21 )[/C][C]2.72427767354595[/C][C]1.07226541636900[/C][C]2.54067475455018[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 21 )[/C][C]2.73128205128204[/C][C]1.04437181185665[/C][C]2.6152391516834[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 21 )[/C][C]2.73904365904365[/C][C]1.00571655555352[/C][C]2.72347476425517[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 21 )[/C][C]2.76769230769230[/C][C]0.962549136582717[/C][C]2.87537768463257[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 21 )[/C][C]2.77254079254078[/C][C]0.91608233316589[/C][C]3.02651922448843[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 21 )[/C][C]2.78124069478907[/C][C]0.879099435136572[/C][C]3.16373846191471[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 21 )[/C][C]2.77389920424402[/C][C]0.83586072769731[/C][C]3.31861410917793[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 21 )[/C][C]2.73213675213674[/C][C]0.80563070678041[/C][C]3.39130165861644[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 21 )[/C][C]2.65969230769230[/C][C]0.774607857779234[/C][C]3.43359840851281[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 21 )[/C][C]2.61812709030099[/C][C]0.755361201523577[/C][C]3.46605979367246[/C][/ROW]
[ROW][C]Median[/C][C]1.88769230769229[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-12.5123076923077[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.49081730769230[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.77254079254078[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.77254079254078[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.77254079254078[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.77254079254078[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.46416289592759[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.77254079254078[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.77254079254078[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]65[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26692&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26692&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-1.10410211956031e-142.01549348282001-5.47807337990239e-15
Geometric MeanNaN
Harmonic Mean-107.722575634686
Quadratic Mean16.1239478625601
Winsorized Mean ( 1 / 21 )-0.00923076923078032.00894988980893-0.00459482303546069
Winsorized Mean ( 2 / 21 )0.1076923076922971.958045778124400.0549998926968167
Winsorized Mean ( 3 / 21 )0.0569230769230661.904737165238040.0298850035385077
Winsorized Mean ( 4 / 21 )0.5123076923076821.760307598187510.291033051743443
Winsorized Mean ( 5 / 21 )1.519999999999991.483251216617611.02477583228698
Winsorized Mean ( 6 / 21 )1.547692307692301.466294059604271.05551290858397
Winsorized Mean ( 7 / 21 )1.644615384615371.400492648950121.17431204358571
Winsorized Mean ( 8 / 21 )1.853846153846141.344231402002711.37911236940617
Winsorized Mean ( 9 / 21 )1.839999999999991.332107403003261.3812700055954
Winsorized Mean ( 10 / 21 )1.978461538461531.299655507382561.52229689115545
Winsorized Mean ( 11 / 21 )2.249230769230761.219630485315151.84419034807052
Winsorized Mean ( 12 / 21 )2.673846153846141.108892979080152.41127521256754
Winsorized Mean ( 13 / 21 )2.673846153846141.108892979080152.41127521256754
Winsorized Mean ( 14 / 21 )2.523076923076911.070826942244492.35619484674942
Winsorized Mean ( 15 / 21 )2.730769230769221.022280560501222.67125223376088
Winsorized Mean ( 16 / 21 )2.706153846153840.9258075796601652.92301975659692
Winsorized Mean ( 17 / 21 )2.836923076923070.8896253616122173.18889635945391
Winsorized Mean ( 18 / 21 )3.086153846153830.7860731649853343.92603892821022
Winsorized Mean ( 19 / 21 )3.261538461538450.7357011207367124.43323840294334
Winsorized Mean ( 20 / 21 )2.953846153846140.6540600894349964.51616938804169
Winsorized Mean ( 21 / 21 )3.018461538461530.6360633248776714.74553620748696
Trimmed Mean ( 1 / 21 )0.3972161172161061.90074595845830.208979067112308
Trimmed Mean ( 2 / 21 )0.8303152585119691.765797485458740.470221112754761
Trimmed Mean ( 3 / 21 )1.228370273793991.632258314186770.752558748279983
Trimmed Mean ( 4 / 21 )1.6736572199731.489759191059561.12344144611898
Trimmed Mean ( 5 / 21 )2.016783216783211.373671804733461.46816962380219
Trimmed Mean ( 6 / 21 )2.138635703918711.332134985122981.60541966677744
Trimmed Mean ( 7 / 21 )2.264162895927591.284998171160041.76199697925141
Trimmed Mean ( 8 / 21 )2.381569858712701.244420910604151.91379768566930
Trimmed Mean ( 9 / 21 )2.472798690671021.208067158795822.04690498592468
Trimmed Mean ( 10 / 21 )2.574358974358961.163912767046112.21181436207837
Trimmed Mean ( 11 / 21 )2.664436493738811.114983213324082.38966511952711
Trimmed Mean ( 12 / 21 )2.724277673545951.072265416369002.54067475455018
Trimmed Mean ( 13 / 21 )2.731282051282041.044371811856652.6152391516834
Trimmed Mean ( 14 / 21 )2.739043659043651.005716555553522.72347476425517
Trimmed Mean ( 15 / 21 )2.767692307692300.9625491365827172.87537768463257
Trimmed Mean ( 16 / 21 )2.772540792540780.916082333165893.02651922448843
Trimmed Mean ( 17 / 21 )2.781240694789070.8790994351365723.16373846191471
Trimmed Mean ( 18 / 21 )2.773899204244020.835860727697313.31861410917793
Trimmed Mean ( 19 / 21 )2.732136752136740.805630706780413.39130165861644
Trimmed Mean ( 20 / 21 )2.659692307692300.7746078577792343.43359840851281
Trimmed Mean ( 21 / 21 )2.618127090300990.7553612015235773.46605979367246
Median1.88769230769229
Midrange-12.5123076923077
Midmean - Weighted Average at Xnp2.49081730769230
Midmean - Weighted Average at X(n+1)p2.77254079254078
Midmean - Empirical Distribution Function2.77254079254078
Midmean - Empirical Distribution Function - Averaging2.77254079254078
Midmean - Empirical Distribution Function - Interpolation2.77254079254078
Midmean - Closest Observation2.46416289592759
Midmean - True Basic - Statistics Graphics Toolkit2.77254079254078
Midmean - MS Excel (old versions)2.77254079254078
Number of observations65


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')